The Human Rights Campaign, the nation’s largest gay rights group, is criticizing President Obama for not naming an openly LGBT cabinet member.

“While the cabinet is full of staunch allies, there is no reason why qualified LGBT Americans willing to serve their country should be overlooked, especially in a day and age when LGBT people are an integral part of the fabric of our nation as everyone from doctors to teachers to professional basketball stars,” HRC spokesman Michael Cole-Schwartz told the Washington Blade Friday, a day after Obama finalized his second-term cabinet appointments. “The president has said it’s our job to remind him when he’s fallen short and while there’s much for which to applaud him, on this issue this president has fallen far short.”

Chuck Wolfe, CEO of the Gay and Lesbian Victory Fund, also said it was disappointing that Obama has not chosen an openly LGBT person for a cabinet appointment. Speaking at the Equality Forum in Philadelphia, he noted that there still could be such an appointment before the president’s second term ends.

White House aide Shin Inouye responded by defending Obama’s record on LGBT issues. “The president is deeply committed to diversity in his administration, and he’s proud of the of LGBT appointments he’s made throughout all levels of his administration,” Inouye told the Blade. “Moreover, he has a strong record of accomplishment on issues of concern to the LGBT community and will continue to make progress in that area.”